An Assessment of FasterAn Assessment of Faster--ThanThan--Light Spacetimes: Make or Break Light Spacetimes: Make or Break Issues Issues (paper AIAA(paper AIAA--20062006--4908)4908)

4242ndnd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, July 9Exhibit, July 9--12, 2006, Sacramento, CA12, 2006, Sacramento, CA

Eric W. Davis, Ph.D., FBISEric W. Davis, Ph.D., FBISInst. for Advanced Studies at AustinInst. for Advanced Studies at Austin

11855 Research Blvd.11855 Research Blvd.Austin, TX 78759Austin, TX 78759

ph: 512ph: 512--342342--2187, FAX: 5122187, FAX: 512--346346--30173017ewdavis@earthtech.orgewdavis@earthtech.org

A Tale of Two FTL Spacetimes in A Tale of Two FTL Spacetimes in General RelativityGeneral Relativity

•• Traversable Wormholes (rich diversity)Traversable Wormholes (rich diversity)

•• Warp Drives (rich diversity)Warp Drives (rich diversity)

•• All other FTL spacetime claims (in GR) are All other FTL spacetime claims (in GR) are spuriousspurious

•• There are wormhole/warp drive spacetimes There are wormhole/warp drive spacetimes in alternative gravity theories & Din alternative gravity theories & D--BraneBrane/quantum gravity theories/quantum gravity theories

Violations of the Energy Violations of the Energy ConditionsConditions

•• HawkingHawking--Ellis “Classical Energy Conditions” Ellis “Classical Energy Conditions” mustmust be be violated to make FTL spacetimes in GRviolated to make FTL spacetimes in GR

•• Energy conditionsEnergy conditions–– Weak Energy Condition (WEC): Weak Energy Condition (WEC): ρρEE ≥≥ 0, 0, ρρEE + p+ pii ≥≥ 00–– Null Energy Condition (NEC): Null Energy Condition (NEC): ρρEE + p+ pii ≥≥ 00–– Dominant (DEC) & Strong (SEC) Energy Conditions are Dominant (DEC) & Strong (SEC) Energy Conditions are

less importantless important

•• All energy condition hypotheses have been All energy condition hypotheses have been experimentally tested in the laboratory & experimentally tested in the laboratory & experimentally shown to be false experimentally shown to be false –– 25 years before 25 years before their formulationtheir formulation–– further investigation showed that violations of energy further investigation showed that violations of energy

conditions are conditions are widespreadwidespread for ALL forms of classical & for ALL forms of classical & quantum matterquantum matter

•• There is no such thing as There is no such thing as ““reasonable matterreasonable matter””

Engineering FTL Spacetimes Engineering FTL Spacetimes Requires Energy Condition Requires Energy Condition Violating “Exotic” MatterViolating “Exotic” Matter

•• So…it’s OK to violate the energy conditions…it’s not So…it’s OK to violate the energy conditions…it’s not a crime against naturea crime against nature

•• Energy densities/fluxes and/or pressures of material Energy densities/fluxes and/or pressures of material required to create FTL spacetimes must be “exotic” required to create FTL spacetimes must be “exotic” (or “negative”)(or “negative”)

•• “Negative” in the sense that material must have: “Negative” in the sense that material must have: energy density energy density ≤≤ pressurespressuresor rather or rather energy density energy density < 0 < 0 (i.e., lower energy than surrounding vacuum)(i.e., lower energy than surrounding vacuum)

→→ ““negativenegative”” is just a misnomeris just a misnomer

Examples of Energy Condition Examples of Energy Condition Violating “Stuff” Found in Nature Violating “Stuff” Found in Nature (or in the Lab)(or in the Lab)

•• Static radiallyStatic radially--dependent electric or magnetic fieldsdependent electric or magnetic fields

•• Squeezed quantum states of the electromagnetic field & Squeezed quantum states of the electromagnetic field & other squeezed quantum fieldsother squeezed quantum fields

•• Gravitationally squeezed vacuum electromagnetic zeroGravitationally squeezed vacuum electromagnetic zero--point fluctuationspoint fluctuations

•• CasimirCasimir Effect in flat or curved spacesEffect in flat or curved spaces

•• Cosmological InflationCosmological Inflation

•• Cosmological Particle ProductionCosmological Particle Production

•• The Conformal AnomalyThe Conformal Anomaly

•• Gravitational Vacuum PolarizationGravitational Vacuum Polarization

Other Examples of Energy Other Examples of Energy Condition Violating “Stuff”Condition Violating “Stuff”

•• Other quantum fields/states/effectsOther quantum fields/states/effects–– In general, the local energy density in quantum field In general, the local energy density in quantum field

theory can be negative due to quantum coherence theory can be negative due to quantum coherence effectseffects

•• Other examples studied: Other examples studied: DiracDirac Field StatesField States

the superposition of two single particle electron the superposition of two single particle electron states and the superposition of two multistates and the superposition of two multi--electronelectron--positron statespositron states

in the former (latter), the energy densities can be in the former (latter), the energy densities can be negative when two single (multinegative when two single (multi--) particle states ) particle states have the same number of electrons (electrons and have the same number of electrons (electrons and positrons) or when one state has one more electron positrons) or when one state has one more electron (electron(electron--positron pair) than the otherpositron pair) than the other

–– To be subject of future studyTo be subject of future study

Lab Examples: Radial Electric or Lab Examples: Radial Electric or Magnetic FieldsMagnetic Fields

Generate Generate radialradial EE-- or Bor B--field field using Ultrahighusing Ultrahigh--Intensity Intensity Lasers (LLNL, UNR, UT):Lasers (LLNL, UNR, UT):

•• power intensity power intensity ≈≈ 10101515 ––10102626 WW//cmcm2 2 (10(103030 WW//cmcm22

using SLAC),using SLAC),peak power pulse peak power pulse ≤≤ 101033 fsfs

•• BB--fields: fields: severalseveral ×× 101066 T, T, ρρmagmag ~~ severalseveral ×× 10101919 J/mJ/m33

•• EE--fields: 10fields: 101414 –– 10101818 VV//mm, , ρρelecelec ≈≈ 10101616 –– 10102828 J/mJ/m33

•• Possible to generate km Possible to generate km –– AU sized wormholes in AU sized wormholes in the lab: the lab: need static E,Bneed static E,B

Lab Examples: (Electromagnetic) Lab Examples: (Electromagnetic) CasimirCasimir EffectEffect

•• Construct (spherically symmetric) wormhole using Construct (spherically symmetric) wormhole using Casimir Effect: two closely spaced, concentric, thin Casimir Effect: two closely spaced, concentric, thin electrically charged hollow spherical plates the size of electrically charged hollow spherical plates the size of Earth’s orbit (~ 10Earth’s orbit (~ 1088 km) to create km) to create negative Casimir energynegative Casimir energy

•• rrwhwh = 1 km: = 1 km: dd = 1.28 = 1.28 ×× 1010−−1616 m (<< nuclear diameter), m (<< nuclear diameter), ρρECEC = = −−4.83 4.83 ×× 10103636 J/mJ/m33

•• rrwhwh = 1 AU: = 1 AU: dd = 1.57 = 1.57 ×× 1010−−1212 m (< electron’s Compton m (< electron’s Compton λλ), ), ρρECEC = = −−2.16 2.16 ×× 10102020 J/mJ/m33

•• Miniscule Miniscule dd unrealistic because unrealistic because CasimirCasimir Effect switches over Effect switches over into noninto non--retarded field behavior (retarded field behavior (~ ~ dd−−33) of van ) of van derder WaalsWaals forces forces when when dd < 15 nm where plates are no longer perfectly < 15 nm where plates are no longer perfectly conductingconducting

( ) ( )( )

11 23 43

18

30

4.05 10 ( )

wh

wh

Gd r c

r meters

π

−

=

= × Morris, Thorne & Yurtsever (1988)

d = cavity plate separationrwh = wormhole throat radius

Lab Examples: Squeezed VacuumLab Examples: Squeezed Vacuum

•• Squeezed vacuum state consists of a traveling Squeezed vacuum state consists of a traveling electromagnetic wave that oscillates back and forth electromagnetic wave that oscillates back and forth between negative and positive energy density, but has between negative and positive energy density, but has positive timepositive time--averaged energy densityaveraged energy density

•• Squeezed Electromagnetic Vacuum:Squeezed Electromagnetic Vacuum:–– moving some quantummoving some quantum--fluctuations of EM field out of fluctuations of EM field out of

coscosωω(t(t −− z/cz/c)) part of the field and into part of the field and into sinsinωω(t(t −− z/cz/c)) partpart

–– one can “squeeze” variance of one observable provided one can “squeeze” variance of one observable provided variance in conjugate observable is stretchedvariance in conjugate observable is stretched

–– observable that gets squeezed will have its fluctuations observable that gets squeezed will have its fluctuations reduced below the vacuum ZPFreduced below the vacuum ZPF

•• Since the vacuum is defined to have vanishing energy Since the vacuum is defined to have vanishing energy density, any region with less energy density than the density, any region with less energy density than the vacuum actually has a negative (renormalized) vacuum actually has a negative (renormalized) expectation value for the energy densityexpectation value for the energy density

Experimental Squeezed Vacuum Experimental Squeezed Vacuum SourceSource

RiesRies, , BrezgerBrezger, , LvovskyLvovsky (2003), “Experimental Vacuum (2003), “Experimental Vacuum Squeezing in Rubidium Vapor via SelfSqueezing in Rubidium Vapor via Self--Rotation,” Rotation,” Phys. Phys. Rev. ARev. A, , 6868, 025801, 025801

“…we demonstrate a simple, scalable squeezed “…we demonstrate a simple, scalable squeezed vacuum source which consists in essence of a vacuum source which consists in essence of a continuouscontinuous--wave (wave (cwcw) diode laser and an atomic ) diode laser and an atomic rubidium vapor cell.”rubidium vapor cell.”

Device Concept: Quantum Optical Device Concept: Quantum Optical “Squeezing” of Light Effect“Squeezing” of Light Effect

- + - + - + - + -

- --

- - - - - -

++

++

++

++

+

Laser & Laser & LiNbOLiNbO33ResonatorResonator

Positive Energy Positive Energy PulsesPulses

Negative EnergyNegative EnergyPulsesPulses

Rotating / RedirectorRotating / RedirectorMirror SystemMirror System

ConcentratedConcentratedNegative EnergyNegative Energy

Squeezed light beam emerges from resonator Squeezed light beam emerges from resonator containing containing pulses of negative energypulses of negative energyinterspersed with pulses of positive energy.interspersed with pulses of positive energy.

Negative/positive energy Negative/positive energy pulses pulses are are ≈≈ 1010−−1515 second second durationduration

Laser beam is passed thru LiNbOLaser beam is passed thru LiNbO33 resonator, which acts resonator, which acts to produce secondary lower frequency beam in whichto produce secondary lower frequency beam in whichpattern of photons is rearranged into pairs.pattern of photons is rearranged into pairs.

Device Concept: Quantum Optical Device Concept: Quantum Optical “Squeezing” of Light Effect“Squeezing” of Light Effect

•• Or a chamber of sodium gas is placed within squeezing Or a chamber of sodium gas is placed within squeezing cavity, and laser beam is directed thru gas:cavity, and laser beam is directed thru gas:

–– beam is reflected back on itself by a mirror to form standing beam is reflected back on itself by a mirror to form standing wave within sodium chamberwave within sodium chamber

–– this wave causes rapid variations in optical properties of the this wave causes rapid variations in optical properties of the sodium thus causing rapid variations in the squeezed light so sodium thus causing rapid variations in the squeezed light so that we can induce rapid reflections of pulses by careful that we can induce rapid reflections of pulses by careful designdesign

Device Concept: Quantum Optical Device Concept: Quantum Optical “Squeezing” of Light Effect“Squeezing” of Light Effect

•• Another way to squeeze light would be to manufacture Another way to squeeze light would be to manufacture extremely reliable light pulses containing precisely one, extremely reliable light pulses containing precisely one, two, three, etc. photons apiece and combine them two, three, etc. photons apiece and combine them together to create squeezed states to order.together to create squeezed states to order.

→→ Superimposing many such states could theoretically Superimposing many such states could theoretically produce produce bursts of intense negative energybursts of intense negative energy..

- - - - - - - - -

Bursts of Intense Negative EnergyBursts of Intense Negative Energy

Single Photon Source in the LabSingle Photon Source in the Lab

RabeauRabeau, J. R., et al. (2004), “Fabrication of single , J. R., et al. (2004), “Fabrication of single nickelnickel--nitrogen defects in diamond by chemical vapor nitrogen defects in diamond by chemical vapor deposition,” arxiv.org/conddeposition,” arxiv.org/cond--mat/0411245mat/0411245RabeauRabeau, J. R., et al. (2004), “Diamond chemical vapor , J. R., et al. (2004), “Diamond chemical vapor deposition on optical fibers for fluorescence deposition on optical fibers for fluorescence waveguidingwaveguiding,” arxiv.org/cond,” arxiv.org/cond--mat/0411249mat/0411249

used a microwave oven to fuse a tiny diamond, just used a microwave oven to fuse a tiny diamond, just 1/10001/1000thth of a millimeter in length, onto an optical fiber, of a millimeter in length, onto an optical fiber, to create a to create a single photonsingle photon beam of lightbeam of light

Traversable WormholesTraversable Wormholes

•• Hyperspace tunnels Hyperspace tunnels thru spacetime, which thru spacetime, which can:can:connect remote regions connect remote regions within our universewithin our universeconnect different connect different universesuniversesconnect different space connect different space dimensions (for higher dimensions (for higher dimensional wormholes)dimensional wormholes)connect different connect different chronological periods chronological periods within the same space within the same space region (time machine!)region (time machine!)

•• This FTL spacetime This FTL spacetime violates the NECviolates the NEC

Negative Energy Engineering for Negative Energy Engineering for Traversable WormholesTraversable Wormholes

Engineering Wormholes: How Engineering Wormholes: How Much Negative MassMuch Negative Mass--Energy is Energy is Required?Required?

Negative Mass Required to Create Wormhole of Given Size Wormhole throat radius, rthroat (meters) Required mass, Mwh

1000 −709.9 MJ 100 −71 MJ 10 −7.1 MJ 1 −0.71 MJ

0.1 −22.6 M⊕ .01 −2.3 M⊕

MJ = 1.90 × 1027 kg, mass of Jupiter M⊕ = 5.98 × 1024 kg, mass of Earth

( )2

0.711

throat throatwh J

r c rM MG meter

= − = −

Warp DrivesWarp Drives

•• AlcubierreAlcubierre plus several plus several incarnations developed:incarnations developed:

Provides for simultaneous Provides for simultaneous expansion of space behind a expansion of space behind a spacecraft & corresponding spacecraft & corresponding contraction of space in front contraction of space in front of spacecraftof spacecraft

World lines inside warp field World lines inside warp field region are spacelike as region are spacelike as viewed by outside observers viewed by outside observers –– gives FTL motion effectgives FTL motion effect

Spacecraft’s moving frame Spacecraft’s moving frame never travels outside its local never travels outside its local comoving light cone, thus comoving light cone, thus does not violate Special does not violate Special RelativityRelativity

•• This FTL spacetime This FTL spacetime violates the WEC & NECviolates the WEC & NEC

Negative Energy Engineering for Negative Energy Engineering for Warp DrivesWarp Drives

Net Total Negative Energy Net Total Negative Energy Required for Warp BubbleRequired for Warp Bubble

(Assume: R = 50 m, σ = 103 m−1)2 4 2

( )

warpwarp

in Joules

v c RE

Gσ

= − Warp Factor, vwarp Required Ewarp(Joules)

10−5 (= 3 km/sec) −3.03 × 1040

10−4 (= 30 km/sec) −3.03 × 1042

0.01 (= 3,000 km/sec) −3.03 × 1046

0.5 (= 150,000 km/sec) −7.59 × 1049

1 (= speed of light) −3.03 × 1050

2 (= 600,000 km/sec) −1.21 × 1051

10 (= 3.0 × 106 km/sec) −3.03 × 1052

100 (= 3.0 × 107 km/sec) −3.03 × 1054

vwarp = dimensionless warp speed

R = radius of warp bubble

σ ∝ 1/∆ (inverse warp bubble wall thickness)

Note: (positive) mass-energy of Sun is 1.79 × 1047 Joules

c = speed of light (3 × 105 km/sec)

Quantum Inequalities ConjectureQuantum Inequalities Conjecture

•• Model dependent time integrals of energy density along Model dependent time integrals of energy density along geodesics geodesics −− for for masslessmassless test particlestest particles–– relates energy density of a free quantum field & time during relates energy density of a free quantum field & time during

which energy density is observedwhich energy density is observed

•• Energy Condition Violating “Stuff” all violate the QIEnergy Condition Violating “Stuff” all violate the QI

•• VisserVisser (1997): O(1997): Observational data indicates that large amounts bservational data indicates that large amounts of “exotic” matter is required to exist in universe to account fof “exotic” matter is required to exist in universe to account for or observed cosmological evolution parameters & halo star ageobserved cosmological evolution parameters & halo star age

•• QI have not been verified by lab experiments or QI have not been verified by lab experiments or observational dataobservational data

•• Assumptions, efficacy of derivations for various cases Assumptions, efficacy of derivations for various cases have been called into question by numerous investigatorshave been called into question by numerous investigators

•• KrasnikovKrasnikov (2005) constructed explicit counterexample for (2005) constructed explicit counterexample for simple, generalized FTL spacetimes showing relevant QI simple, generalized FTL spacetimes showing relevant QI do not holddo not hold

•• Therefore, we will ignore the QI conjectureTherefore, we will ignore the QI conjecture

Superior Quantifier for Energy Superior Quantifier for Energy Condition Violations & Negative Condition Violations & Negative EnergyEnergy

•• Spatial volume (definite) Spatial volume (definite) integrals:integrals:

–– Measures both WEC & Measures both WEC & NEC violationsNEC violations

–– Amount of WEC/NEC Amount of WEC/NEC violation is defined as violation is defined as extent to which integrals extent to which integrals become negativebecome negative

–– Value of integrals Value of integrals provides info about total provides info about total amount of WEC/NEC amount of WEC/NEC violating matter must be violating matter must be used to build any FTL used to build any FTL spacetime

–– Integrals can be adjusted Integrals can be adjusted to become vanishingly to become vanishingly small by appropriate small by appropriate choice of parameterschoice of parameters

–– Examples can be Examples can be constructed whereby constructed whereby violations can be made violations can be made arbitrarily small arbitrarily small –– but not but not vanish entirelyvanish entirely

( );E E idV p dVρ ρ +∫ ∫spacetime ρE = energy density

pi = pressuresdV = 4πr2dr or (gmetric)1/2 dr dθ dϕ

Case 1: Traversable Wormholes Case 1: Traversable Wormholes ––A New Requirement on Negative A New Requirement on Negative EnergyEnergy

•• ALLALL Traversable Wormhole spacetimes now Traversable Wormhole spacetimes now only require only require arbitrarily smallarbitrarily small quantities of quantities of negative massnegative mass--energy (energy (VisserVisser, , KarKar and and DadhichDadhich, 2003):, 2003):

0 ( )rp dV radial pressure volume integral→∫

0Eρ =

NOTE: NNOTE: Nonlinearity of Einstein field equations dictates that onlinearity of Einstein field equations dictates that the total massthe total mass--energy of the wormhole system energy of the wormhole system ≈≈ 00

Additional Constraints on Additional Constraints on Traversable WormholesTraversable Wormholes

•• Detailed energy analysis Detailed energy analysis & nonlinearity of Einstein & nonlinearity of Einstein field field eqnseqns. impacts . impacts coupling of finite coupling of finite spacecraft mass w/ each spacecraft mass w/ each side of a wormhole’s side of a wormhole’s throat (or the mouth on throat (or the mouth on each side of the throat)each side of the throat)

•• Specialized mass Specialized mass conservation law for conservation law for combined system of combined system of spacecraft & wormhole:spacecraft & wormhole:

–– finite mass spacecraft finite mass spacecraft traversing a wormhole traversing a wormhole alters the (equivalent) alters the (equivalent) mass of the wormhole mass of the wormhole mouths they pass throughmouths they pass through

•• Entrance mouth absorbing Entrance mouth absorbing spacecraft gains (equiv.) spacecraft gains (equiv.) mass while exit mouth mass while exit mouth emitting it loses (equiv.) emitting it loses (equiv.) massmass

•• Suggests, but does not Suggests, but does not prove, the possibility of prove, the possibility of fundamental limit on total fundamental limit on total mass that can traverse a mass that can traverse a wormholewormhole

•• For sufficiently large net For sufficiently large net transfer of mass the final transfer of mass the final (equiv.) mass of exit (equiv.) mass of exit mouth becomes negativemouth becomes negative

•• Beneficial result because Beneficial result because NEC violations are NEC violations are required to hold wormhole required to hold wormhole throat openthroat open

Case 2: Warp DrivesCase 2: Warp Drives

•• AlcubierreAlcubierre & other warp drive incarnations are flawed: & other warp drive incarnations are flawed: only consider spaceship as only consider spaceship as masslessmassless test particle moving test particle moving on geodesic, not coupled to warp bubbleon geodesic, not coupled to warp bubble

•• Correct approach: finite mass spaceship coupled to warp Correct approach: finite mass spaceship coupled to warp bubblebubble–– net total energy stored in warp field < total massnet total energy stored in warp field < total mass--energy of energy of

spaceshipspaceship–– intrinsic nonlinearity of Einstein field equationsintrinsic nonlinearity of Einstein field equations–– gives powerful constraint on warp speedgives powerful constraint on warp speed–– can only achieve can only achieve absurdly low subabsurdly low sub--light speedslight speeds for any for any

reasonable engineering parametersreasonable engineering parameters

( )1

228

27.41 10 shipwarp

Mv

R−⎡ ∆ ⎤⎛ ⎞

≤ ×⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦ R = radius of warp bubble

Mship = mass of spaceship

∆ = warp bubble wall thickness

Observing Negative Energy: Observing Negative Energy: Optical MethodOptical Method

•• Produces unique Produces unique signature corresponding signature corresponding to lensing, chromaticity to lensing, chromaticity and intensity effects in and intensity effects in micromicro-- and macroand macro--lensing lensing events on galactic, events on galactic, extragalactic, extragalactic, cosmological scalescosmological scales

•• Effects provide specific Effects provide specific signature allowing for signature allowing for discrimination between discrimination between ordinary and negative ordinary and negative energy lenses via spectral energy lenses via spectral analysis of astronomical analysis of astronomical lensing eventslensing events

•• Real background sources Real background sources in lensing events can in lensing events can have nonhave non--uniform uniform brightness distributions brightness distributions on their surfaces and a on their surfaces and a dependency of their dependency of their emission with the emission with the observing frequencyobserving frequency

–– these complications these complications result in chromaticity result in chromaticity effects, i.e. in spectral effects, i.e. in spectral changes induced by changes induced by differential lensing during differential lensing during the eventthe event

•• Must be developed for labMust be developed for lab--scale experimentsscale experiments

Observing Negative Energy: NonObserving Negative Energy: Non--Optical MethodOptical Method

•• Response of switched Response of switched particle detectors to particle detectors to static negative energy static negative energy densities/fluxes:densities/fluxes:–– based on free based on free

((masslessmassless) scalar field ) scalar field in flat 4in flat 4--dimensional dimensional Minkowski spacetimeMinkowski spacetime

–– standard monopole standard monopole detector switched detector switched on/off to concentrate on/off to concentrate measurements on measurements on periods of isolated periods of isolated negative energy negative energy density/fluxdensity/flux

–– includes switching includes switching factor, 5 switching factor, 5 switching functions evaluatedfunctions evaluated

•• Result: Negative energy Result: Negative energy has effect of enhancing has effect of enhancing deexcitationdeexcitation ((induce induce coolingcooling) of a detector) of a detector

•• Cannot draw firm Cannot draw firm conclusion because conclusion because modeling is only 1modeling is only 1stst order order in perturbation theory:in perturbation theory:

–– not possible to predict if not possible to predict if enhanced cooling is due enhanced cooling is due to small violation of to small violation of energy conservation energy conservation expected in any process expected in any process in which a general in which a general quantum state collapses quantum state collapses to an energy to an energy eigenstateeigenstate

–– or if it is a systematic or if it is a systematic reduction in the energy of reduction in the energy of detectordetector

ConclusionConclusion•• Two forms of FTL spacetimes identified by Einstein’s GR: Two forms of FTL spacetimes identified by Einstein’s GR:

traversable wormholes & warp drivestraversable wormholes & warp drives–– require introduction of negative energy densities/fluxes to implrequire introduction of negative energy densities/fluxes to implementement

•• Detailed energy analysis shows that Detailed energy analysis shows that allall warp drives are not warp drives are not technologically practical to implementtechnologically practical to implement–– high total negative energyhigh total negative energy →→ absurdly low subabsurdly low sub--light speedslight speeds

•• Detailed energy analysis shows that traversable wormholes Detailed energy analysis shows that traversable wormholes appear to be the most practical to implementappear to be the most practical to implement–– arbitrarily small amounts of negative energy requiredarbitrarily small amounts of negative energy required

•• We already make small amounts of negative energy in the labWe already make small amounts of negative energy in the lab–– don’t know if we can access larger amounts for extended periods don’t know if we can access larger amounts for extended periods of of

time over extended spatial distributionstime over extended spatial distributions

•• Proposals for optical observation of negative energy in outer Proposals for optical observation of negative energy in outer spacespace–– further work is needed to downscale astronomical techniques for further work is needed to downscale astronomical techniques for use use

at the lab scaleat the lab scale

•• Need to firm up our understanding of how nonNeed to firm up our understanding of how non--optical lab optical lab detectors will respond to negative energy in situdetectors will respond to negative energy in situ